Graph-based causal discovery methods aim to capture conditional independencies consistent with the observed data and differentiate causal relationships from indirect or induced ones. Successful construction of graphical models of data depends on the assumption of causal sufficiency: that is, that all confounding variables are measured. When this assumption is not met, learned graphical structures may become arbitrarily incorrect and effects implied by such models may be wrongly attributed, carry the wrong magnitude, or mis-represent direction of correlation. Wide application of graphical models to increasingly less curated "big data" draws renewed attention to the unobserved confounder problem. We present a novel method that aims to control for the latent space when estimating a DAG by iteratively deriving proxies for the latent space from the residuals of the inferred model. Under mild assumptions, our method improves structural inference of Gaussian graphical models and enhances identifiability of the causal effect. In addition, when the model is being used to predict outcomes, it un-confounds the coefficients on the parents of the outcomes and leads to improved predictive performance when out-of-sample regime is very different from the training data. We show that any improvement of prediction of an outcome is intrinsically capped and cannot rise beyond a certain limit as compared to the confounded model. We extend our methodology beyond GGMs to ordinal variables and nonlinear cases. Our R package provides both PCA and autoencoder implementations of the methodology, suitable for GGMs with some guarantees and for better performance in general cases but without such guarantees.
翻译:基于图表的因果发现方法旨在捕捉与观察到的数据相一致的有条件依赖性,并将因果关系与间接或诱发的因果关系区别开来。成功构建图形数据模型取决于对因果关系是否充分这一假设的假设:即所有混杂变量都得到测量。如果这一假设没有实现,学习的图形结构可能会成为任意错误,而这种模型隐含的影响可能会被错误地归结,产生错误的规模,或错现的因果关系方向。广泛应用图形模型来预测越来越少的“大数据”会重新引起人们对未观察到的混淆问题的注意。我们提出了一个新颖的方法,目的是在通过迭接地从推断模型的剩余部分中提取潜在空间的代理物来估算DAG时控制潜在空间。根据温和的假设,我们的方法可以改进高斯图形模型的结构推理,提高因果效应的可辨性能。此外,在使用模型来预测结果的母性系数时,它并不混淆,结果母体的预测性能会改善,当超出标定的离子系统时,我们无法对数值作更精确的预测,因此,我们无法对数值进行更精确的数值分析。